Efficient In-Network Computing with Noisy Wireless Channels

In this paper, we study distributed function computation in a noisy multihop wireless network. We adopt the adversarial noise model, for which independent binary symmetric channels are assumed for any point-to-point transmissions, with (not necessarily identical) crossover probabilities bounded above by some constant $(\epsilon)$. Each node takes an $(m)$-bit integer per instance, and the computation is activated after each node collects $(N)$ readings. The goal is to compute a global function with a certain fault tolerance in this distributed setting; we mainly deal with divisible functions, which essentially cover the main body of interest for wireless applications. We focus on protocol designs that are efficient in terms of communication complexity. We first devise a general protocol for evaluating any divisible functions, addressing both one-shot $((N = O(1)))$ and block computation, and both constant and large $(m)$ scenarios. We also analyze the bottleneck of this general protocol in different scenarios, which provides insights into designing more efficient protocols for specific functions. In particular, we endeavor to improve the design for two exemplary cases: the identity function, and size-restricted type-threshold functions, both focusing on the constant $(m)$ and $(N)$ scenario. We explicitly consider clustering, rather than hypothetical tessellation, in our protocol design.